document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=688869>Question 688869</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How do i find the Center, Vertices, Foci and the Equation of the asymptotes of the following equation<BR>\n" );
document.write( "(((x-2)^2)/25)-(((y-1)^2)/9) = 1 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #425715 by </B><A HREF=/tutors/aboutme.mpl?userid=lwsshak3><B>lwsshak3(11628)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=lwsshak3><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=425715\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> How do i find the Center, Vertices, Foci and the Equation of the asymptotes of the following equation<BR>\n" );
document.write( "(((x-2)^2)/25)-(((y-1)^2)/9) = 1<BR>\n" );
document.write( "This is an equation of a hyperbola with horizontal transverse axis. (x-term listed first)<BR>\n" );
document.write( "Its standard form of equation: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1 ALIGN=MIDDLE  ALT=\"%28x-h%29%5E2%2Fa%5E2-%28y-k%29%5E2%2Fb%5E2=1\"   DISABLED_style= \"max-width:90%; height:auto;\" >, (h,k)=(x,y) coordinates of center<BR>\n" );
document.write( "For given equation: (x-2)^2)/25)-(y-1)^2)/9)=1<BR>\n" );
document.write( "center: (2,1)<BR>\n" );
document.write( "a^2=25<BR>\n" );
document.write( "a=&#8730;25=5<BR>\n" );
document.write( "vertices:(2±a,1)=(2±5,1)=(-3,1) and (7,1)<BR>\n" );
document.write( "b^2=9<BR>\n" );
document.write( "b=&#8730;9=3<BR>\n" );
document.write( "c^2=a^2+b^2=25+9=34<BR>\n" );
document.write( "c=&#8730;34&#8776;5.8<BR>\n" );
document.write( "foci:(2±c,1)=(2±5.8,1)=(-3.8,1) and (7.8,1)<BR>\n" );
document.write( "asymptotes: (straight line equations that go thru center, y=mx+b, m=slope, b=y-intercept)<BR>\n" );
document.write( "slopes of asymptotes for hyperbolas with horizontal transverse axis=±b/a=±3/5<BR>\n" );
document.write( "Equation of asymptote with negative slope: <BR>\n" );
document.write( "y=-3x/5+b<BR>\n" );
document.write( "solve for b using coordinates of center(2,1)<BR>\n" );
document.write( "1=-3*2/5+b<BR>\n" );
document.write( "b=1+6/5=11/5<BR>\n" );
document.write( "equation: y=-3x/5+11/5<BR>\n" );
document.write( "..<BR>\n" );
document.write( "Equation of asymptote with positive slope: <BR>\n" );
document.write( "y=3x/5+b<BR>\n" );
document.write( "solve for b using coordinates of center(2,1)<BR>\n" );
document.write( "1=3*2/5+b<BR>\n" );
document.write( "b=1-6/5=-1/5<BR>\n" );
document.write( "equation: y=-3x/5-1/5<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );